The production of mixtures of di- and polyamines of the diphenylmethane series (MDA) with the principal component diaminodiphenylmethane (diamines) by reaction of aniline with formaldehyde in the presence of acid catalysts is generally known. The di- and polyamine mixtures are widely used predominantly for the production of the corresponding di- and polyisocyanate mixtures. Examples for continuous or partially discontinuous processes are disclosed in U.S. Pat. No. 5,286,760, EP-A-451442 and WO-A-99/40059. Therein it is in fact mentioned that after neutralization of the acid reaction mixture, phase separation and optionally washing with water, adhering water and excess aniline is removed distillatively, normally under vacuum. These disclosures do not however give any indication of the significance of the contents of water and aniline for the further use of the di- and polyamines for the production of the corresponding di- and polyisocyanates. Also, in the literature no processes for achieving these low contents of water and aniline are described. Also there is no indication in the literature of how the distillation of the di- and polyamines with separation of aniline and water can be energetically optimized. A further problem area is the return of the separated aniline to the reaction, wherein according to EP-A-0283757 as far as possible no MDA should be returned to the reaction with formaldehyde.